GPS is a navigation system composed of satellites in orbit and ground stations, for example, GPS receivers, for receiving signals from the satellites. With GPS, one can determine the location of any ground station by analyzing signals from multiple satellites. Typically, each GPS satellite used for position determination includes a transmitter and a precision clock. The GPS satellites transmit a spread-spectrum GPS signal containing time and implicit carrier phase information. A ground station receives the GPS signal and the time the signal was sent. The GPS receiver can use arrival time and phase of each GPS satellite signal to calculate the location of the receiver by determining how far away each satellite is from the receiver.
As is known, a single measurement is generally not adequate to determine the position of the GPS receiver. As such, GPS receivers often perform a process known as trilateration, wherein multiple signals and transmission times are used to determine the three-dimensional position of the receiver. If three GPS signals and corresponding transmission times are known, the GPS receiver can generally determine a location, depending on how satellites are distributed in the sky and whether the receiver can use certain assumptions regarding a known location parameter (e.g. altitude) to remove unknowns in the trilateration computation. Four satellites are usually needed to determine both location and elevation of the receiver. In the event that the GPS receiver does not have an accurate clock, the fourth satellite can be used to make the measured location more precise by correcting some of the clock error. The fourth satellite may also be used to determine an elevation, though the errors in determining elevation are typically greater than the errors that can arise in determining latitude and longitude.
Unfortunately, calculating exact distances on the Earth and converting them to latitude/longitude coordinates is a complicated process and generally requires the use of complicated expressions provided by the U.S. Geological Survey, which are quite complex. The earth is not spherical, but rather, an irregular mass that more closely approximates a biaxial ellipsoid than a sphere. The two radii of the earth, the polar radius and the equatorial radius, respectively, range from about 6,356.75 km to about 6,378.14 km, or about 3,949.9 miles to about 3,963.19 miles. Because of the surface irregularities, complex datasets exist to be used by GPS receivers to estimate elevation based upon an approximated radius of the earth at the current location. These complicated data sets, specific for granular regions of the Earth's surface, are generally relied upon not only for elevation determination, but also to obtain an accurate representation of the distance between two points. Using these methods and datasets can result in more accurate position determinations, but can be a computationally intensive process.
During movement of the GPS receiver, readings can be taken at intervals to reflect movement. In general, the GPS receiver can calculate and display the current location as long as the GPS receiver can receive GPS signals. At times, however, the GPS receiver cannot receive GPS signals and may not be able to accurately calculate and display the current location. For example, if the GPS receiver enters a tunnel, a built-up area such as, for example, a city with tall buildings, an area with irregular terrain, or another location in which the GPS satellites are out of the GPS receiver's line of sight, it is possible to lose a satellite fix and, consequently, the ability of the GPS receiver to determine the current location of the GPS receiver.
In such areas, an alternative method of obtaining coordinates through extrapolation of position can be useful. When a GPS fix is lost, some known GPS receivers attempt to estimate a current position based upon a prior location, a known speed and bearing, and known map data. For example, an automobile with a GPS navigation system may display a position even when GPS signals have been lost, e.g., in a tunnel. Some GPS navigation systems accomplish this by using the last known position, bearing, speed, and map data to estimate current location. When the GPS signals are again acquired, there can be typically a correction step to move the estimated location to the actual location.
The applicants have discovered that errors in excess of 5-10 meters are common when using such methods of extrapolation. While errors of 5-10 meters can be adequate for automobile navigation, in which a driver still relies upon roads to guide the vehicle, errors of this magnitude can be too great for fine applications in which more precise measurements are needed.